Problem: Divide. Write your answer in simplest form. $ \dfrac{1}{9} \div \dfrac{5}{4} = {?} $
Answer: Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $\dfrac{5}{4}$ is $\dfrac{4}{5}$. Therefore: $ \dfrac{1}{9} \div \dfrac{5}{4} = \dfrac{1}{9} \times \dfrac{4}{5} $ $ \phantom{\dfrac{1}{9} \div \dfrac{5}{4}} = \dfrac{1 \times 4}{9 \times 5} $ $ \phantom{\dfrac{1}{9} \div \dfrac{5}{4}} = \dfrac{4}{45} $